Search with terms filter in 1.4.2

Appologies if this has been covered but couldn't find the answer I was looking for. I'm attempting to filter search results by a specific content type and multiple taxonomy terms. I understand queries and projections could probably get me what I want but I'm
stuck on ver 1.4.2 for various reasons. I'd basically just like to filter search results by multiple terms across multiple taxonomies.

The code fragment (SearchController.cs) below is my first attempt at retrieving a specific taxonomy and term;

try
{
// Ok, I know how to find the taxonomy and term I'm interested in
var taxonomy = _taxonomyService.GetTaxonomyByName("Finish");
var term = _taxonomyService.GetTermByName(taxonomy.Id, "Cherry");
// This would get me the specific content items for the first term,
// but how would I introduce a second term
var query = _taxonomyService.GetContentItemsQuery(term);
// This is the original search that I'd like to replace using the new query
// filtered by mutiple terms from separate taxonomies
searchHits = _searchService.Query(q, pager.Page, pager.PageSize,
Services.WorkContext.CurrentSite.As<SearchSettingsPart>().Record.FilterCulture,
searchFields,
searchHit => searchHit);
}